Infrared measuring gauges

ABSTRACT

An infrared gauge for, and a method of, measuring a parameter of a sample, e.g. moisture content or sample thickness, the gauge comprising: 
     a source of infrared radiation directed at the sample, 
     a detector for detecting the amount of infrared radiation transmitted, scattered or reflected from the sample at at least one measuring wavelength and at at least one reference wavelength, wherein the parameter absorbs infrared radiation at the at least one measuring wavelength and absorbs a lesser amount of infrared radiation at the at least one reference wavelength, and an algorithm processing unit for calculating the value of the parameter of interest from the intensity of radiation detected by the detector at the measuring and the reference wavelengths, the value of the parameter of interest being calculated according to the following equation:        P   =           a   0     +     ∑       a   i          f        (     S   i     )                 b   0     +     ∑       b   i          f        (     S   i     )               +     c   0                       
      where: 
     P is the predicted value of the parameter concerned, for example film thickness or moisture content; 
     a 0 , b 0  and c 0  are constants; 
     i is  1, 2, 3  . . . and denotes the different wavelengths used; 
     S i  is the signal produced when the sample is exposed to a given wavelength i; 
     a i  and b i  are constants; and 
     f(S i ) stands for a transformation applied to the signal S i . 
     This provides improved accuracy of measuring the parameter.

The present invention relates to infrared absorption gauges and inparticular to the analysis of signals produced from such gauges tomeasure a parameter of a sample under investigation.

Infrared absorption gauges are well-known and used for example formeasuring constituents of samples (e.g. the moisture content of paper ortobacco, or the fat, protein and water contents of foodstuffs), theamounts of substances absorbed or adsorbed on a substrate, the thicknessof coatings or films on a substrate or the degree of cure of resins in aprinted circuit board. In this specification, the term “parameter” isused to denote the property (composition, coating thickness etc.) of thesample being measured.

Infrared absorption gauges operate by projecting infrared radiation attwo or more wavelengths onto a sample or substrate and measuring theintensity of radiation reflected, transmitted or scattered by thesample. Signals proportional to the measured intensity are processed toprovide a value of the parameter being measured. At least one of the twomore wavelengths projected by the gauge is chosen to be absorbed by theparameter of interest while the other wavelength is chosen to besubstantially unaffected by the parameter of interest. For example, whenmeasuring the amount of water in a sample, one of the wavelengths (the“measuring wavelength”) can be chosen at an absorption wavelength ofwater (either 1.45 micrometre or 1.94 micrometre) and the otherwavelength (known as the “reference wavelength”) is not significantlyabsorbed by water.

Generally, gauges include an infrared radiation source having a broademission spectrum and a detector for receiving radiation reflected,scattered or transmitted by the sample; filters are placed between thesource and the sample to expose the sample only to the desired measuringand reference wavelengths; in this case, the sample is successivelyexposed to radiation at the selected wavelengths, e.g. by placingappropriate filters on a rotating wheel in front of the radiationsource. Alternatively (but less preferably), the filters can be placedbetween the sample and the detector and each filter is successivelyinterposed between the sample and the detector. Naturally, if the sourcecan produce radiation of the desired wavelength without the use offilters, then such filters can be dispensed with.

The detector measures the intensity of light after interaction with thesample and produces a signal according to the intensity of the radiationincident upon it. In the most simple case, by calculating the ratiobetween the signal from the detector when receiving light at themeasuring wavelength to that when receiving light at the referencewavelength, a signal can be obtained that provides a measure of theparameter concerned, for example the amount of moisture in a sample.Often, several measuring wavelengths and/or several referencewavelengths are used and the signals of the measuring wavelengths and ofthe reference wavelengths are used to calculate the parameter concerned.

In fact, conventionally, the value of the parameter is calculatedaccording to the following algorithm (I):$P = {a_{0} + {\sum\limits_{i = {1n}}\quad {a_{i}\log \quad S_{i}}}}$

where:

is the predicted value of the parameter concerned, for example filmthickness or moisture content;

a_(o) is a constant;

i is 1, 2, 3 . . . and denotes the different wavelengths used;

n is the number of wavelengths used in the gauge;

S_(i) is the signal produced when the sample is exposed to a givenwavelength i; and

as is a constant to be applied to signal S_(i.)

The above formula can be derived from the Beer-Lambert law fornon-scattering materials. The base of the logarithms in the abovealgorithm is immaterial because the value of the constants a_(i) can bescaled according to the basis of the logarithm used.

The constants a_(o) and a_(i) can be calculated from a so-called“calibration” set of data, which is a set of infrared absorption datafrom a range of samples whose parameter of interest is known (so-called“reference samples”); thus by measuring the signals produced when eachof the reference samples is exposed at each wavelength, the constantsa_(o) and a_(i) can be calculated by solving a straightforward set ofsimultaneous equations. It is possible to simplify the calculation byapplying a constraint that the sum of the constants a_(i) should equalzero. In fact, it is exceedingly unlikely that a single set of constantsa₀ and a_(i) will produce an exact fit across the whole range ofparameter values and therefore the constants a₀ and a_(i) are calculatedto produce the “best fit” to the data obtained in the calibration set,for example the constants are set to give the minimum residual standarddeviation (rsd) for the data concerned. The calibration set of datashould be obtained from samples having parameters across the whole rangeof parameters that will, in practice, be encountered when using theinfrared gauge.

It will be appreciated that the accuracy of the infrared gauge can beimproved by increasing the number of wavelengths that the gauge uses.However, this greatly adds to the expense, complexity and response timeof the gauge and accordingly it is desirable to provide an alternativemethod for improving the accuracy of infrared gauges.

We have found that it is possible to greatly improve the accuracy of aninfrared gauge by the use of a new algorithm (II) as follows:$P = {\frac{a_{0} + {\sum{a_{i}{f\left( S_{i} \right)}}}}{b_{0} + {\sum{b_{i}{f\left( S_{i} \right)}}}} + c_{0}}$

where:

P is the predicted value of the parameter concerned, for example filmthickness or moisture content;

a₀ b₀ and c₀ are constants;

i is 1, 2, 3 . . . and denotes the different wavelengths used;

n is the number of wavelengths used in the gauge;

S_(i) is the signal produced when the sample is exposed to a givenwavelength i;

a_(i) and b_(i) are constants; and

f(S_(i)) stands for a transformation applied to the signal S_(i); thistransformation could be a log function, log (1/S) or, indeed, thetransformation could be an identity transformation, i.e. notransformation at all). In the latter case, the algorithm would bealgorithm (III):$P = {\frac{a_{0} + {\sum{a_{i}S_{i}}}}{b_{0} + {\sum{b_{i}S_{i}}}} + c_{0}}$

In the algorithm of the present invention, it is not necessary to useall the signals to calculate the numerator or the denominator, in whichcase the value of any constant a_(i) or b_(i) would be set at zero.

According to one aspect of the present invention, there is provided aninfra red gauge for measuring a parameter of a sample, the gaugecomprising:

a source of infrared radiation directed at the sample,

a detector for detecting the amount of infrared radiation transmitted,scattered or reflected from the sample at at least one measuringwavelength and at at least one reference wavelength, wherein theparameter absorbs infrared radiation at the said at least one measuringwavelength and absorbs a lesser amount of infrared radiation at the saidat least one reference wavelength,

means for calculating the value of the parameter of interest from theintensity of radiation detected by the detector at the measuring and thereference wavelengths, the value of the parameter of interest beingcalculated according to the following equation:$P = {\frac{a_{0} + {\sum{a_{i}{f\left( S_{i} \right)}}}}{b_{0} + {\sum{b_{i}{f\left( S_{i} \right)}}}} + c_{0}}$

 where:

P is the predicted value of the parameter concerned, for example filmthickness or moisture content;

a₀, b₀ and c₀ are constants;

i is 1, 2, 3 . . . and denotes the different wavelengths used;

S_(i) is the signal produced when the sample is exposed to a givenwavelength i;

a_(i) and b_(i) are constants; and

f(S_(i)) stands for a transformation applied to the signal S_(i.)

According to another aspect of the present invention there is provided amethod of measuring the value of a parameter in a sample, the methodcomprising:

directing infrared radiation at the sample,

measuring the intensity of infrared radiation reflected, scattered ortransmitted by the sample at at least a first wavelength (measuringwavelength) and at at least a second wavelength (reference wavelength),the parameter absorbing infrared radiation at the said measuringwavelength(s) and being less absorbing at the said referencewavelength(s), and

calculating the value of the parameter of interest from the intensity ofradiation detected by the detector at the measuring and the referencewavelengths, the value of the parameter of interest being calculatedaccording to the following equation:$P = {\frac{a_{0} + {\sum{a_{i}{f\left( S_{i} \right)}}}}{b_{0} + {\sum{b_{i}{f\left( S_{i} \right)}}}} + c_{0}}$

 where:

P is the predicted value of the parameter concerned, for example filmthickness or moisture content;

a₀, b₀ and c₀ are constants;

i is 1, 2, 3 . . . and denotes the different wavelengths used;

S_(i) is the signal produced when the sample is exposed to a givenwavelength i;

a_(i) and b_(i) are constants to be applied to signal S_(i); and

f(S_(i)) stands for a transformation applied to the signal S_(i).

Our current understanding of the benefits obtained from using Algorithms(II) and (III) are that the numerator part of the algorithm provides aprediction of the parameter of interest, but, as with conventionalalgorithms, shows different measurement sensitivities for materialswhere the mean effective path length of light through the material canvary. The effect can occur, for example, where the light scatteringcharacteristics of the material varies, or, the thickness of thematerial varies independently to the parameter of interest. The purposeof the denominator in the algorithm is then to compensate for factorswhich affect the measurement sensitivity.

A simple example is in the measurement of percentage moisture in paper,where the mass per unit area of the base material is not constant. Thenumerator would produce values proportional to the total mass of watercontent observed, and the denominator would produce values proportionalto the corresponding total mass of the base material observed.

It is difficult to calculate the optimum constants used in algorithms IIand III by theoretical methods and therefore an empirical method isusually necessary, whereby an iterative numerical procedure is used tofit, constants when a calibration data set of samples with knownparameter values, is employed.

The invention will now be described further, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 is a schematic section through the head of an infrared gaugeaccording to the present invention;

FIG. 2 is a schematic block diagram of the circuitry of the infraredgauge according to the present invention;

FIG. 3 is a diagrams for illustrating the selection of the constants inone particular example according to the present invention;

FIGS. 4 to 7 are graphs representing a particular worked example of thepresent invention.

Referring initially to FIGS. 1 and 2, FIG. 1 shows the head 10 of aninfrared gauge according to the present invention. The head 10 containsa lamp 12 providing a source of infrared radiation, a broad emissionspectrum and a circular filter wheel 14 driven by a motor 16.

The filter wheel 14, further illustrated in FIG. 2, carries a series offilters 18, in this instance five such filters. Each filter 18 isdesigned to pass a different selected emission wavelength.

Light passed by a respective filter 18 is arranged to strike a beamsplitter 20 which reflects a portion of the light beam downwardly out ofthe infrared gauge 10 towards a sample 22. A remaining portion of theinfrared light beam striking the beam splitter 20 is refracted withinthe beam splitter towards a primary detector 24 in the form of aphoto-electric sensor. Meanwhile, the light emitted by the head 10towards the sample 22 is reflected back from the sample 22 towards acollecting mirror 26 in the head 10 and thence to a secondary detector28 in the form of another photo-electric sensor. The two detectors 24,28 thus generate detection signals representing, respectively, theintensity of the light emitted by the lamp 12 and filtered by a selectedone of the filters 18, and the intensity of that same light afterreflection from the sample 22. The detection signals in the presentinstance are voltage signals.

Referring to FIG. 2, the voltages output by the detectors 24, 28 in useare first amplified by respective amplifiers 30, 32 and then convertedinto binary form by respective A/D converters 34, 36. The binary signalsoutput by the A/D converters 34, 36 are both supplied to a centralprocessing unit (CPU) 38, to be described in greater detail below, forgenerating at a main output 40 a signal representing the parameterconcerned.

Before the infrared gauge can be used to measure a parameter in thesample 22, however, it is necessary to locate one or more measuringwavelengths and reference wavelengths. This is usually accomplished bytaking infrared spectra of various samples, employing for example aspectrophotometer, and locating (a) those wavelengths which varystrongly with any variation in the parameter of interest to locate themeasuring wavelengths and (b) those wavelengths which vary only weakly(or not at all) with any variation in the parameter of interest tolocate the reference wavelengths. After the required wavelengths havebeen selected, the appropriate filters 18 are incorporated into thefilter wheel 14 of the infrared gauge of head 10.

A “calibration” set of values is then used in the described infraredgauge to calculate the value of the constants a₀, b₀, a_(i) and b_(i) inalgorithm (II) above. This involves the taking of a large number ofsamples whose parameter is of a known value. It will be appreciated thatthe number of samples required will increase with the number ofwavelengths used and it is estimated that at least forty samples shouldbe used to compile the calibration set when three wavelengths aremeasured in the gauge, seventy samples should be used when fourwavelengths are used in the gauge, and a hundred samples should be usedwhen five wavelengths are used in the gauge. The voltage signalsgenerated by the detectors 24, 28 at each wavelength for each sample arethen used to calculate the constants in algorithm (II) of the presentinvention using the methods and software described below.

For each such sample whose parameter is of a known value, the sample isplaced under the infrared gauge head 10 and for each respective filter18 voltage, signals are supplied from the detectors 24, 28 to the CPU38. The signals Q1 to Q5 obtained from the primary detector 24 afteramplification and A/D conversion are stored in a FIFO memory array 42,and the corresponding signals RI to R5 obtained from the secondarydetector 28 are stored in a FIFO memory array 44.

Entry of the binary values from the two detectors 24, 28 into the twomemory arrays 42, 44 is synchronised by means of a synchronising signalsource 46 shown schematically in FIG. 2. Essentially, this synchronisingsignal source 46 comprises a photo-electric emitter and photo-electricsensor positioned on opposite sides of the filter wheel 14 just insideits circumference. The filter wheel 14 itself has a series of smallholes formed at a constant angular spacing throughout the extent of itscircumference, with the exception that at one point of the circumferencetwo of the holes are positioned closely adjacent one another at asignificantly reduced angular spacing. A control unit within thesynchronising signal source 46 drives the motor 16 and monitors thepassage of the two closely adjacent holes and then the number of holesthat subsequently pass the photo-electric emitter to provide anindication as to which filter 18 is in front of the light source 10 andto ensure that the binary signals are stored in the arrays 42, 44 inrespective storage locations corresponding to each filter 18.

Once binary signals corresponding to each of the filters 18 have beenstored in the memory arrays 42, 44 for any particular sample whoseparameter is of a known value, then signals SI to S5 are calculated fromthese binary values in an arithmetic control unit 48 and aresubsequently stored in a further memory array 50. The signal S in eachcase is derived in the arithmetic unit 48 by dividing the binary value Robtained from the secondary detector 28 by the corresponding binaryvalue Q obtained from the primary detector 24. In the exampleillustrated, there are five filters 18 and, therefore, there will befive values S1 to S5 eventually stored in the memory array 50. At thisstage, these values are supplied to a secondary output 52 forcalculation of the constants a_(o), b_(o), a_(i) and b_(i) by comparingthe measured values S1 to S5 from each sample whose parameter is knownwith the known value for that parameter.

Several suitable numerical procedures are known for determiningconstants, a_(o), b_(o), a_(i) and b_(i), of which some are available inthe form of computer software. Such methods include the “steepestdescent” method, the “inverse-Hessian” method, the “Levenberg-Marquardt”method and the “full Newtonian” method. These methods are fullydescribed in “Numerical Recipes in C” by Press, Teukonsky, Vetterling &Flannery (published by Cambridge University Press).

The full Newtonian method is the most complex and gives the mostreliable results but it requires a large computing capacity and takes along time to arrive at values for the constants. Accordingly, we preferto use the “steepest descent” or the “Levenberg-Marquardt” methods.

Levenberg-Marquardt software is commercially available in the followingcomputer packages:

1) LabVIEW produced by National Instruments Corporation of 6504 BridgePoint Parkway, Austin, Tex. 78730-5039, USA or

2) Statgraphics produced by STSC Inc., 2115 East Jefferson Street,Rockville, Md. 20852, USA; and

3) “Numerical Recipes in C” (software routines can be purchased with thebook of the same title mentioned above).

It is not necessary to describe precisely how the above computerpackages calculate the constants but it can be visualised in the case ofa simplified version of algorithm II that contains only two constants,a₁ and b₁: the values of a₁ and b₁ for a given sample could be plottedalong X and Y axes and the “accuracy” of the value P calculated fromalgorithm II for the different values of a₁ and b₁ could be plottedalong the Z axis; the “accuracy” plotted along the Z axis would be thedifference between the value of P calculated from solving the algorithmand the actual value of the parameter in the sample. The resulting plotwould be a three-dimensional surface and the desired values of a₁ and b₁would be those where the plot had a minimum, i.e. where the accuracy isgreatest (or the deviation from the value of the actual parameter is theleast). An example of such a plot is shown in FIG. 3.

The easiest to visualise of the above-described methods for calculatingthe “best fit” values of the constants (i.e. the values of the constantsthat minimises the difference between the calculated value of theparameter P and the value of the actual parameter in the sample) is the“steepest descent” method. Applying that method to find the minima inthe plot described in the previous paragraph, a pair of values for thetwo constants a₁ and b₁ is initially selected as a “guestimate”; (a=2,b=2, in FIG. 3) the steepest gradient of the plot at the pointcorresponding to the initial values of a₁ and b₁ is calculated (shown byarrow W in FIG. 3). The direction of the steepest gradient with the plotgives after a pre-determined distance two new values for a₁ and b₁. Thesteepest gradient of the plot at the point corresponding to the newvalues of a₁ and b₁ is then calculated and the direction of the steepestgradient with the plot gives two further values for a₁ and b₁. Thisprocess is repeated until the desired minimum is reached (a=7, b=4 inFIG. 3).

The Levenberg Marquardt method also uses an iterative process butinstead estimates, from the shape of the plot at a given pair ofconstants a₁ and b₁ where the minimum is likely to be. It then performsa similar operation at the point of the plot where the minimum waspredicted to be; this procedure is continued until the actual minimum islocated. The Levenberg Marquardt method generally uses a fewer number ofiterative steps and is therefore to be preferred.

It will be appreciated that the plot may have several local minima andit may well be necessary to validate that any minimum found is in factthe true minimum of the plot by repeating the iterative process fromseveral starting values of the constants a₁ and b₁ concerned.

The above graphical representation of the plot is a vastover-simplification of the actual calculation of the constants inalgorithm II since many more than two constants will be present andhence the “plot” will have more than 3 dimensions.

At this point, it should be mentioned that the LabVIEW package mentionedabove contains a univariate routine which will have to be modified tomake it multi-variate before it can applied to the calculation of theconstants. However, the Statgraphics package mentioned above ismulti-variate and therefore no such modification is required.

Once the constants have been determined from the calibration set ofsamples using one of the procedures described above, then a processingunit 54 in the CPU 38 is set up to perform algorithm (II) using theseconstants.

After this, a further set of samples is then used to ensure that theoverall readings given by the gauge are accurate; this is the so-called“validation set” of samples. The parameter of interest is also known forthese samples and the value P is calculated in processing unit 54 fromalgorithm (II) from the signals S1 to S5 obtained by submitting thesesamples to measurement by the infrared gauge. Obviously, if the valuesof the parameter obtained at output 40 from the samples in thevalidation set do not comply with the known values to an acceptabledegree of accuracy, then the calibration step must be repeated.

After validation, the infrared gauge incorporating the algorithm of thepresent invention can be used to predict from the signals produced bythe infrared radiation detectors 24, 28 of the gauge the parameter ofinterest, for example polymer film thickness or water content in paperor fat content in meat, and to supply such parameter to main output 40

It is well-known that infrared gauges can measure either the infraredlight transmitted by a sample or the infrared light reflected orscattered from a sample. The algorithm of the present invention isapplicable to all such methods.

The parameters that can be measured according to the present inventioninclude not only the proportion of a given substance in a material (forexample the percentage moisture content in paper or the percentage fatcontent in meat) but also the thickness of a coating on a material (forexample the thickness of adhesive on a paper substrate).

It will be appreciated that the algorithm according to the presentinvention can be incorporated into a more complex algorithm having thesame general effect as algorithm (II). The present invention alsoextends to the use of such more complex algorithms.

The use of the algorithms of the present invention are particularlybeneficial when measuring highly scattering substrates, particularlypaper.

Example 1

The diffuse reflectant infrared spectra of 37 widely-varying types ofpaper, each having 10 different moisture content levels in the range 3.5to 9.5%, were collected. The actual moisture content of these papers (socalled “reference values”) were obtained using an oven referencetechnique by which the moisture-containing paper is weighed, it is thenplaced in an oven to dry out, and the dried paper is then weighed again.From the change in the weight of paper, the initial moisture content canbe calculated.

The papers used ranged in weight from 40 to 400 g per square metre andincluded glassine, mechanical paper, Kraft paper and chemical paper ofdifferent types. From an analysis of the spectra, various wavelengthswere selected for use in a gauge. The Applicants have developed computersoftware that simulates the response of a gauge containing interferencefilters centred on two or more wavelengths of the spectrum that lookpromising. The simulation convolves the spectrum over each selectedwavelength with a 1.6% bandwidth gaussian function to simulate theeffect, in the gauge, of the use of an optical interference filter witha “full width, half maximum” bandwidth of 1.6% of the centre wavelength.The computer software can also calculate the values of the constants a₀,b₀, c₀, a_(i)and b_(i) in algorithm (II) above for the sample concernedfor a set of selective combinations of wavelengths. From theseconstants, it is possible to estimate the accuracy of the measurement onthe paper samples for each combination of wavelengths to locate anoptimum set of filters for use in the gauge. Using this simulationtechnique, five wavelengths were selected at 1817, 1862, 1940, 2096 and2225 nm. However, it is not necessary to select the wavelengths usingsuch a simulation technique and the wavelengths can be selected merelyby examining the spectra of the samples and choosing appropriatemeasuring and reference wavelengths.

Optical interference filters centred on the above five wavelengths wereincorporated into an infrared gauge and a calibration set of data wasobtained. From this, the constants as, b₀, c₀, a_(i) and b_(i) inalgorithm (II) above (in which f(S_(i))=log S_(i)) or algorithm III werecalculated and the accuracy of the algorithm to predict the actualvalues of the parameter in the reference samples was calculated. Theresults were expressed as the percentage of moisture in the varioussamples falling within one standard deviation of the value predictedfrom the algorithm. The results were as follows:

conventional algorithm (I) 0.507% algorithm (II), where f(S_(i)) = logS_(i) 0.331% algorithm (III) 0.335%

These improvements could not be achieved using conventional algorithm Iand simply increasing the number of measurement wavelengths used in agauge. For example, when using twelve different wavelengths in aconventional algorithm, an accuracy of only 0.44% moisture to onestandard deviation was observed.

Example 2

The infrared spectra of 37 different types of paper, each at 10different moisture levels between 1% and 10% wet weight moisture, weremeasured in a diffuse reflectance spectrophotometer. By examination ofthe spectral data and from information published, five suitablemeasurement wavelengths were selected. These were as follows: 1.7micrometres (first neutral reference), 1.8 micrometres (second neutralreference), 1.94 micrometres (water absorption band), 2.1 micrometres(cellulose absorption band), and 2.2 micrometres (third neutralreference). Optical interference filters centred at these wavelengthswere manufactured and fitted into the filter wheel 14 of an infraredabsorption gauge as detailed earlier.

In this example, a set of 6 paper samples, with a wide range of weightper unit area, were selected to include in a calibration set. Eachsample was presented to the gauge at several different moisturecontents, and the signals, S1 to S5, were recorded. The weight of eachsample was measured at the time of signal recording, and subsequentlythe actual % moisture content (so called “reference values”) of thesesamples were calculated by drying them completely in an electric ovenand calculating the weight loss as a percentage of the wet weight.

The applicants then employed computer software based on LabVIEW, whichincorporates an iteration routine described earlier, to determine theoptimum values of constants a₀, b₀, c₀, a_(i) and b_(i) for algorithm(I) and (II) in order to predict the parameter of interest from theinfrared gauge signals S1 to S5. In this example, the gauge signal dataand the corresponding reference values were used in the software tocalculate the optimum constants for algorithm (II) to predict percentagemoisture. Various combinations of between 2 and 5 filter signals weretested in the numerator and in the denominator part of the algorithm.The best results were as follows:

Filter wavelength Constant (micrometers) Constant Value a₁ 2.2 0 a₂ 1.726 a₃ 1.8 0 a₄ 1.94 −37 a₅ 2.1 11 a₀ 3 b₁ 2.2 0 b₂ 1.7 −2.4 b₃ 1.8 5.3b₄ 1.94 0 b₅ 2.1 −2.9 b₀ 1 c₀ 0.75

These constants gave a standard error value of 0.288% and a correlationcoefficient of 0.986. An XY graph of these is shown in FIG. 4.

The numerator part of the algorithm without the denominator partcompensating for the effect of different measurement sensitivities forthe different papers, results in noticeably different slopes fordifferent papers, depending upon the weight and type. This is showngraphically in FIG. 5.

The compensating output of the denominator part of the algorithm isshown in FIG. 6. As shown, this part of the algorithm is not sensitiveto variation in the paper moisture.

It is useful to compare the output P for a conventional Algorithm (I)and the output P for Algorithm (II), using the same filter wavelengths.The optimised constants for this example set of data using Algorithm (I)are given below:

Filter wavelength Constant (micrometers) Constant value a₁ 2.2 0 a₂ 1.70.82 a₃ 1.8 0 a₄ 1.94 −3.36 a₅ 2.1 2.54 a₀ 6.63

These constants gave a standard error value of 0.881% and a correlationcoefficient of 0.866. An XY graph of these is shown in FIG. 7 below. Itcan be seen that, although the standard deviation of errors about thebest-fit line are minimised, the different sensitivities to paper weightand type remain.

What is claimed is:
 1. An infrared gauge for measuring a parameter of asample, the gauge comprising: a source of infrared radiation directed atthe sample, a detector for detecting the amount of infrared radiationtransmitted, scattered or reflected from the sample at at least onemeasuring wavelength and at at least one reference wavelength, whereinthe parameter absorbs infrared radiation at the said at least onemeasuring wavelength and absorbs a lesser amount of infrared radiationat the said at least one reference wavelength, means for calculating thevalue of the parameter of interest from the intensity of radiationdetected by the detector at the measuring and the reference wavelengths,the value of the parameter of interest being calculated according to thefollowing equation:$P = {\frac{a_{0} + {\sum{a_{i}{f\left( S_{i} \right)}}}}{b_{0} + {\sum{b_{i}{f\left( S_{i} \right)}}}} + c_{0}}$

 where: P is the predicted value of the parameter concerned, for examplefilm thickness or moisture content; a₀, b₀ and c₀ are constants; i is 1,2, 3 . . . and denotes the different wavelengths used; S_(i) is thesignal produced when the sample is exposed to a given wavelength i;a_(i) and b_(i) are constants; and f(S_(i)) stands for a transformationapplied to the signal S_(i).
 2. A gauge as claimed in claim 1, whereinthe function f(S) is a log function or a log (1/S) function.
 3. A gaugeas claimed in claim 1, wherein the algorithm is an algorithm (III):$P = {\frac{a_{0} + {\sum{a_{i}S_{i}}}}{b_{0} + {\sum{b_{i}S_{i}}}} + {c_{0}.}}$


4. A method of measuring the value of a parameter in a sample, themethod comprising: directing infrared radiation at the sample, measuringthe intensity of infrared radiation reflected, scattered or transmittedby the sample at at least a first wavelength (measuring wavelength) andat at least a second wavelength (reference wavelength), the parameterabsorbing infrared radiation at the said measuring wavelength(s) andbeing less absorbing at the said reference wavelength(s), andcalculating the value of the parameter of interest from the intensity ofradiation detected by the detector at the measuring and the referencewavelengths, the value of the parameter of interest being calculatedaccording to the following equation:$P = {\frac{a_{0} + {\sum{a_{i}{f\left( S_{i} \right)}}}}{b_{0} + {\sum{b_{i}{f\left( S_{i} \right)}}}} + c_{0}}$

 where: P is the predicted value of the parameter concerned, for examplefilm thickness or moisture content; a₀, b₀ and c₀ are constants; i is 1,2, 3 . . . and denotes the different wavelengths used; S_(i) is thesignal produced when the sample is exposed to a given wavelength i;a_(i) and b_(i) are constants to be applied to signal S_(i); andf(S_(i)) stands for a transformation applied to the signal S_(i).
 5. Amethod as claimed in claim 4, wherein the function f(S_(i)) is a logfunction or a log (1/S_(i)) function.
 6. A method as claimed in claim 4,wherein the algorithm is an algorithm III$P = {\frac{a_{0} + {\sum{a_{i}S_{i}}}}{b_{0} + {\sum{b_{i}S_{i}}}} + {c_{0}.}}$